Both are used in Japanese. Onyomi is the Chinese reading (not really Chinese, but an approximation of the original pronuncation) and kunyomi is the Japanese reading. The onyomi reading is usually used for kanji compounds (several characters in a row) while the kunyomi reading is usually used for the kanji by itself. (Though, there are exceptions to these rules.) As an example, Kunyomi: 今 ima, meaning "now"; 月 tsuki, meaning "moon". If these kanji aren't next to other kanji they're read this way. However... Onyomi: 今月 kongetsu, meaning "this month". The onyomi reading in this case for 今 is kon, the one for 月 is getsu. You should learn at least one of both the kunyomi and onyomi readings when learning the kanji. Sometimes several kanji can be next to eachother and read with the kunyomi anyway, like 今行きます。(行く iku=to go) meaning "I'm going now." You'll get a feel for these different readings as you study more Japanese.